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HRSB, 2009 TI-83, TI-83 TI-83, TI-83 + + Technology Technology Integration Integration DAY 1 DAY 1 Data Management Data Management
HRSB, 2009
TI-83, TI-83TI-83, TI-83++
Technology Technology IntegrationIntegration
DAY 1DAY 1
Data ManagementData Management
HRSB, 2009
HRSB, 2009
Basic TI-83 KeysBasic TI-83 Keys OnOn – Play Time! (5 – Play Time! (5
min)min) Multifunction keysMultifunction keys Screen brightness Screen brightness ^
Negative vs. subtractNegative vs. subtract(-) -(-) -
Arithmetic operationsArithmetic operations
Clear vs. QuitClear vs. Quit
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The Home Screen and The Home Screen and BEDMASBEDMAS
It’s a calculator!It’s a calculator! 6 + 3 * 4 = 186 + 3 * 4 = 18
It remembers stuff!It remembers stuff!ENTRY (2ENTRY (2ndnd ENTER) ENTER)ANS (2ANS (2ndnd (-)) (-)) STOSTO22nd,nd, entry, STO, X, entry, STO, X,
ENTER – ENTER – xx22+2x+1, +2x+1, ENTERENTER
It changes stuff! It changes stuff! (123456)(123456)DEL – highlight and DEL – highlight and DELDELINS (2INS (2ndnd DEL) DEL)CLEAR – line, CLEAR – line,
homesreenhomesreen
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The Home Screen and The Home Screen and BEDMASBEDMAS
BEDMASBEDMAS rules! rules!BBracketsrackets
EExponentsxponents
DDivisionivision (in (in order they order they
occur) occur)
MMultiplicationultiplication
AAddition ddition
SSubtractionubtraction
Brackets are extremely Brackets are extremely important!important!
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Key ConsiderationsKey Considerations MemoryMemory – Resetting; Clearing Lists/entries – Resetting; Clearing Lists/entries ‘‘The Big Five’The Big Five’ – – Mode:Mode:
Normal Normal SCI SCI (power 10)(power 10) ENG ENG
Digits both left and right of decimalDigits both left and right of decimal 1 Digit left of decimal1 Digit left of decimal up to 3 up to 3 digitsdigits
CatalogCatalog, , MathMath TI-83/83+ KEY List (handout)TI-83/83+ KEY List (handout)
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DATA DATA MANAGEMENTMANAGEMENT
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The Central Measures of The Central Measures of TendencyTendency(p.14 Booklet)(p.14 Booklet)
Describing the DataDescribing the DataAverageAverage: a number that is typical of a set of : a number that is typical of a set of
numbers. numbers. There are three There are three ways of measuring the average:ways of measuring the average:
(1)(1) Mean ( )Mean ( )
(2)(2) MedianMedian
(3)(3) ModeMode
XX
X
X
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The Mean ( )The Mean ( ) Also commonly known as the ‘average’Also commonly known as the ‘average’ Calculated by dividing the Calculated by dividing the sumsum of the of the
data set by the data set by the numbernumber of data values of data values in the set.in the set.
EX: EX: What is the class average (to the nearest whole What is the class average (to the nearest whole number), given the following test scores?number), given the following test scores?
1616 1818 2020 2020 2222 2424 2424 2828 2828
= = = =
= 22= 22
X
ofscores
scores
#X X
9
200
9
200
X
The MedianThe Median The The middle valuemiddle value in a data set, when in a data set, when
arranged in order from arranged in order from leastleast to to greatestgreatest..
(a)(a) Odd number of data scoresOdd number of data scores
33 8 8 12 12 15 15 1515 15 15 17 17 18 18 23 23
LeastLeast ↑↑ GreatestGreatest
middlemiddle
(b)(b) Even number of data scoresEven number of data scores
33 8 12 14 8 12 14 15 1715 17 18 20 21 18 20 21 23 23
LeastLeast ↑↑ ↑↑ GreatestGreatest
middlesmiddles
)(162
1715Median
)(162
1715Median
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The ModeThe Mode
The measurement that occurs the The measurement that occurs the most often in a set of data scores.most often in a set of data scores.
You can have more than one mode You can have more than one mode for a data set.for a data set.
It is possible to have NO mode for a It is possible to have NO mode for a set of data scores.set of data scores.
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The RangeThe Range
The difference between the largest The difference between the largest data value and the smallest data data value and the smallest data value within a particular data set.value within a particular data set.
EX: EX: 22 44 44 88 88 1515 2121
RangeRange: 21 – 2 = 19: 21 – 2 = 19
Activity Time – Yellow Page 1Activity Time – Yellow Page 1
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Measures of Central Measures of Central Tendency:Tendency:
Using the CalculatorUsing the Calculator1] For each set of data determine the mean, 1] For each set of data determine the mean,
median, mode and range. Express your median, mode and range. Express your answers to two decimal places. answers to two decimal places. (see (see Yellow Page 2 for calc. instructions)Yellow Page 2 for calc. instructions)
(a)(a) 20, 24, 28, 18, 26, 24, 12, 16, 2020, 24, 28, 18, 26, 24, 12, 16, 20(b)(b) 5, 9, 13, 12, 2, 4, 0, 1, 7, 15, 115, 9, 13, 12, 2, 4, 0, 1, 7, 15, 11
2] Calculate the mean, median, mode and 2] Calculate the mean, median, mode and range for the following data set:range for the following data set:
12.5, 12.4, 12.2, 12.7, 12.9, 12.2, 12.3, 12.2, 12.5, 12.4, 12.2, 12.7, 12.9, 12.2, 12.3, 12.2, 12.6, 12.812.6, 12.8
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Answers:Answers:
[1][1](a) mean: 20.89, median: 20.00, mode: 20 & (a) mean: 20.89, median: 20.00, mode: 20 &
2424
(b) mean: 7.18, median: 7.00, mode: no (b) mean: 7.18, median: 7.00, mode: no modemode
[2][2] mean: 12.48, median: 12.45, mode: 12.2mean: 12.48, median: 12.45, mode: 12.2
Now try: “The Central Measures of “The Central Measures of Tendency (A)”Tendency (A)” – yellow worksheetyellow worksheet
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The Central Measures of The Central Measures of Tendency (A)Tendency (A)
StudeStudentnt
MeanMean MediMedianan
ModeMode
AlysiaAlysia 84.8884.88%%
85.5085.50%%
NoneNone
LauriLauriee
79.1379.13%%
83.0083.00%%
90.0090.00%%
AhmeAhmedd
78.8378.83%%
84.5084.50%%
NoneNone(b) Alysia
(c) Graduation Average: Alysia – 86.33%; Laurie – 85.17%; Ahmed – 78.83%
(d) Both Alysia and Laurie
(e) Laurie; Both other students…Fate is sealed!
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The Central Measures of The Central Measures of Tendency (B)Tendency (B)
(A)(A) Mean: 9.33Mean: 9.33
Median: size 10Median: size 10
Mode: 10Mode: 10
(b) Discussion(b) Discussion
(c) Discussion(c) Discussion
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ExtensionExtension: : pg.212 Grade 8 Textpg.212 Grade 8 TextMathematics 8 – Focus & Mathematics 8 – Focus &
UnderstandingUnderstanding Yellow Page 5 – Table Groups Yellow Page 5 – Table Groups
(Check on Overhead)(Check on Overhead) Last week Mr. Brighton measured the Last week Mr. Brighton measured the
heights of his seven prized oak seedlings. heights of his seven prized oak seedlings. He noted that the range of the heights He noted that the range of the heights was 6.20 cm and that his tallest seedling was 6.20 cm and that his tallest seedling measured 10.80 cm. The mean height measured 10.80 cm. The mean height was 7.40 cm, the median height was 7.60 was 7.40 cm, the median height was 7.60 cm, and the mode was 8.00 cm. What cm, and the mode was 8.00 cm. What could be the heights of all seven could be the heights of all seven seedlings?seedlings?
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Extension Answer (s)Extension Answer (s)(Many solutions)(Many solutions)
IE:IE:
4.64.6 5.8 7 7.6 8 8 5.8 7 7.6 8 8 10.810.8
________ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____ ____
Must Have:Must Have:
4.6 ____ ____ 7.6 ____ ____ 10.84.6 ____ ____ 7.6 ____ ____ 10.8
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Box and Whisker PlotsBox and Whisker Plots (pg.15-16 Booklet)(pg.15-16 Booklet)
Orange Sheet 1Orange Sheet 1 A type of graph used to display data; shows A type of graph used to display data; shows
how the data is dispersed around the median how the data is dispersed around the median butbut does not show specific scores in the data. does not show specific scores in the data.
Key terms:Key terms:
- - Lower and Upper ExtremesLower and Upper Extremes – Max & Min Value – Max & Min Value
- - Lower QuartileLower Quartile – The median of the lower half – The median of the lower half of of the data the data
- - Upper QuartileUpper Quartile – The median of the upper half – The median of the upper half of of the data the data
How to Construct a Box and How to Construct a Box and Whisker PlotWhisker Plot
1] Construct a # line and mark the upper and lower 1] Construct a # line and mark the upper and lower extremes. The difference between extremes extremes. The difference between extremes represents the range.represents the range.
2] Find the median of the data. Mark this value on # 2] Find the median of the data. Mark this value on # line.line.
3] Find the lower quartile. Mark this value on the # 3] Find the lower quartile. Mark this value on the # line.line.
4] Find the upper quartile. Mark this value on the # 4] Find the upper quartile. Mark this value on the # line.line.
5] Construct a box to show where the middle 50% of 5] Construct a box to show where the middle 50% of the data are located. the data are located. (Now try Orange Sheet 2)(Now try Orange Sheet 2)
English Assignment English Assignment Results…Results…
Now let’s display the same data using the TI-83+…50, 50, 50, 50, 50, 50, 50 60, 60, 60, 60, 60, 60, 60 70, 70, 70,. 70, 70, 70, 70
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ActivityActivity: “Who do we want on : “Who do we want on our Team?”our Team?”
Orange Page 3Orange Page 3 Complete in Table groups and discuss Complete in Table groups and discuss
your resultsyour results
Debrief (next slide)Debrief (next slide)
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““Who do we want on our Who do we want on our Team?”Team?”Anne
Susan
Sonya
Discussion:
- Middle 50% of the data (the spread)
- Consistency
- Outliers
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Box and Whisker Plots – Box and Whisker Plots – Exercise (A)Exercise (A)
In table groups complete the “Raisin In table groups complete the “Raisin Activity” using the TI-83+Activity” using the TI-83+
Discuss your results with table Discuss your results with table membersmembers
Debrief – next slideDebrief – next slide
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Box & Whisker plots:Box & Whisker plots:Using the CalculatorUsing the Calculator
Exercise A:Exercise A: Brand A
Brand B
b) Discussion
c) Discussion
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Box & Whisker plots:Box & Whisker plots:Using the CalculatorUsing the Calculator
Exercise B: [1]Exercise B: [1] Light BulbsLight Bulbs
Brand A
Brand B
Exercise B: [2] Television
(a)Median- 8
(b)Range – Between 6 – 11 hours
(c)Discussion
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Histograms Histograms (pg. 17-18 booklet)(pg. 17-18 booklet)
Another way to display data; used when there are Another way to display data; used when there are many pieces of continuous datamany pieces of continuous data
Comprised of a graph in which the Comprised of a graph in which the horizontal axishorizontal axis is a #line with values grouped in is a #line with values grouped in BinsBins (classes), (classes), and and vertical axisvertical axis shows the shows the frequencyfrequency of the data of the data within each bin.within each bin.
BinBin: a grouping of the data values (i.e. 0 – 5): a grouping of the data values (i.e. 0 – 5) Frequency TableFrequency Table: shows how often each data : shows how often each data
value, or group of values, occurs. value, or group of values, occurs.
BINBIN FREQUENCYFREQUENCY
0 – 50 – 5 # of times a value between 0 & # of times a value between 0 & 5 occurs, not including 55 occurs, not including 5
5 – 105 – 10 # of times a value between 5 & # of times a value between 5 & 10 occurs, not including 1010 occurs, not including 10
10 - 1510 - 15 # of times a value between 10 # of times a value between 10 & 15 occurs, not including 15& 15 occurs, not including 15
Frequency Table (i.e.)
How to Make a Histogram1. Choose a bin size based on your range of data
values. (keep # of bins to ≤10) – Discuss
2. Create a Frequency Table showing group frequencies.
3. Graph the frequency table; connect the bins together in a ‘Bar-graph’ fashion. (let’s try exercise A, Blue Sheet 1)
Histograms ex. AHistograms ex. A
2 6 17 12 24 22 9 10 3 24 2 6 17 12 24 22 9 10 3 24
5 13 8 14 21 20 11 8 19 75 13 8 14 21 20 11 8 19 7
Bin Sizes: Bin Sizes: 0 – 5, 5 – 10, 10 – 15, 15 – 20, 20 – 250 – 5, 5 – 10, 10 – 15, 15 – 20, 20 – 25
Frequency Table: Frequency Table: BinsBins FrequencyFrequency
0 – 50 – 5 22
5 – 105 – 10 66
10 – 1510 – 15 55
15 – 2015 – 20 22
20 – 2520 – 25 55
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Histogram (A)Histogram (A)
FrequencyFrequency
0 5 10 15 20 250 5 10 15 20 25
BinsBins
Histograms (B)Histograms (B)
PossibilitiesPossibilities: : What do we see in each case?What do we see in each case?
#1 - #1 - #2 - #2 - BinsBins Freq.Freq.30-4030-40 22
40-5040-50 77
50-6050-60 77
60-7060-70 88
BinsBins Freq.Freq.30-3530-35 22
35-4035-40 00
40-4540-45 55
45-5045-50 22
50-5550-55 22
55-6055-60 55
60-6560-65 77
65-7065-70 11
Let’s use the technology to create a histogram for “Nancy’s Basketball scores” on Blue Sheet 3…(sketch)
Calculator Applications Calculator Applications (pg 17-18 Booklet):(pg 17-18 Booklet):
NancyNancy JohnJohn SamSam
1] Describe each of the Histograms.
2] Describe each person as a basketball player.
3] Compare these players with Janie’s Data distribution:
Janie
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Histogram Extension ProblemHistogram Extension Problem
Blue Sheet 4Blue Sheet 4 In table groups, complete the ‘Black In table groups, complete the ‘Black
Spruce Tree’ activitySpruce Tree’ activity Discuss resultsDiscuss results
Refer to solution on next slideRefer to solution on next slide
Extension Problem Extension Problem (Discussion)(Discussion)
Forest Environment VS. Nursery EnvironmentForest Environment VS. Nursery Environment
Forest:Forest:
Nursery:Nursery:
Scatter plots – Scatter plots – Line of Best FitLine of Best FitRegression!Regression!
A graph of ordered pairs of numeric dataA graph of ordered pairs of numeric data Used to see relationships between two variables or Used to see relationships between two variables or
quantitiesquantities Helps determine the Helps determine the correlation correlation between the between the
Independent & dependent variablesIndependent & dependent variables CorrelationCorrelation: a measure of how closely the points on : a measure of how closely the points on
a scatter plot fit a linea scatter plot fit a line The relationship can be strong, weak, positive or The relationship can be strong, weak, positive or
negativenegative + Correlation – As indep.Var + Correlation – As indep.Var ↑, Dep. Var ↑↑, Dep. Var ↑ - Correlation – As indep. Var ↑, Dep. Var ↓- Correlation – As indep. Var ↑, Dep. Var ↓
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Line of Best FitLine of Best Fit Drawn through as many data points as possibleDrawn through as many data points as possible Aim to have an equal amount of data points above Aim to have an equal amount of data points above
and below the lineand below the line Does NOT have to go through the originDoes NOT have to go through the origin Allows us to generate an equation that describes Allows us to generate an equation that describes
the relationship using an equation form the relationship using an equation form (ie: y = mx+b)(ie: y = mx+b)
Example 1, Pink Sheet 1Example 1, Pink Sheet 1 – – Discuss (draw LOBF for each)Discuss (draw LOBF for each)
Example 2, Pink Sheet 1, Example 2, Pink Sheet 1, Let’s do together Let’s do together using theusing the
TI-83+TI-83+
Calculator Applications: Calculator Applications: 10.10.(pg. 38-42 Booklet)(pg. 38-42 Booklet)
Example 2: Line of Best FitExample 2: Line of Best Fit
1.1. 2. 2. 3. 3.
4.4. 5. 6. 5. 6.
7.7. 8. 9. 8. 9.
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Linear Regression & Correlation Coefficient Linear Regression & Correlation Coefficient (r) (r)
Determining the Equation for the Line of best fit can be Determining the Equation for the Line of best fit can be referred to as: referred to as: Regression AnalysisRegression Analysis
We create a model that can be used to predict values of the We create a model that can be used to predict values of the Dep. Var. based on values of the Indep. Var.Dep. Var. based on values of the Indep. Var.
The ‘r’ value – Correlation CoefficientThe ‘r’ value – Correlation Coefficient
- measures the strength of the association of the 2 variables;- measures the strength of the association of the 2 variables;
(-1 (-1 → +1) – the closer to either, the stronger the relationship→ +1) – the closer to either, the stronger the relationship
Pink Sheet 3Pink Sheet 3 – – complete in table groups –complete in table groups –
(steps on page 4, 5 pink sheets)(steps on page 4, 5 pink sheets)
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Regression AnalysisRegression AnalysisPg.383, Gr. 9 Text, #13Pg.383, Gr. 9 Text, #13
WindowWindow Scatter plot Scatter plotCorrelationCorrelation
EquationEquation GraphGraph
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Extrapolating data:Extrapolating data: Determining # injured in 2010:Determining # injured in 2010:Change ‘window’ to include this x parameterChange ‘window’ to include this x parameter(Xmax – 2050) The new graph:(Xmax – 2050) The new graph:Next Key Strokes:Next Key Strokes:22ndnd CALC 1:value CALC 1:value
Type in 2010Type in 2010
Y value when x = 2010, is Y value when x = 2010, is
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Regression Analysis Cont.Regression Analysis Cont.
Example 3, 4: Pink Sheet 3 -Example 3, 4: Pink Sheet 3 - EXTENSIONEXTENSION
- Looking at Parabolic & Exponential Looking at Parabolic & Exponential RelationshipsRelationships
- Complete these problems togetherComplete these problems together
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THE ENDTHE END Q & AQ & A Possibilities for further extension on TI-83+Possibilities for further extension on TI-83+ Suggestions for future PD sessionsSuggestions for future PD sessions Wrap-up; Sub Claim FormsWrap-up; Sub Claim Forms
Contact InformationContact Information::Sohael AbidiSohael Abidi
Leader, MathematicsLeader, MathematicsHalifax Regional School BoardHalifax Regional School Board
Ph: 464-2000 ext. 4456Ph: 464-2000 ext. [email protected]@hrsb.ns.ca
